This invention relates to nuclear reactors of the kind having a core composed of closely packed parallel fuel elements which are provided with bearing pads at selected levels whereby the elements are firmly positioned against one another to prevent them rattling. Such a nuclear reactor core is disclosed in U.S. Pat. No. 3,383,287 and the fuel elements in that reactor core are arranged in groups in each of which each element is supported in such a manner as to tend to tilt the element towards the centre of the respective group whereby the elements of each group are urged laterally into firm engagement either with one another or with a structural member around which the group may be arranged. Thus the elements of each group are jammed together, and, where desirable, about a central post on which the surrounding elements lean.